Nucleon-level Effective Theory of Muon to Electron Conversion in Nuclei*

The observation of neutrino flavor oscillations shows that lepton flavor is not conserved in nature, raising the question of whether similar phenomena will be found among the charged leptons. For this reason, new experiments to search for µ-to-e conversion - a muon bound in a 1s orbital around a nucleus converts into an outgoing mono-energetic electron – are a high priority at Fermilab (Mu2e) and J-PARC (COMET).

As any positive observation of charged lepton flavor violation will require some extension of the SM, one would like to better understand how measurements of this low-energy process will constrain models of BSM physics. To make contact with nuclear structure, the low-energy effective operators for µ-to-e conversion must ultimately be reduced to the nucleon level. We formulate the most general nucleon-level effective theory describing µ-to-e conversion in the nuclear field. The low-energy constants of this theory represent the most general constraint that µ-to-e conversion in nuclei can impose on a given UV theory. We present the effective theory and estimate the constraints which can be obtained if next-generation experiments achieve their design sensitivity.